Problem: Rewrite as a simplified fraction. ${0.8\overline{4} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 84.4444...\\ 10x &= 8.4444...\end{align*}}$ Subtracting the two equations, we have: ${90x = 76}$ ${x = \dfrac{76}{90}} $ ${x = \dfrac{38}{45}} $